Atanassov's Intuitionistic Fuzzy Ideals of Gamma Semigroups

TL;DR

This paper explores Atanassov's intuitionistic fuzzy set theory applied to gamma semigroups, providing new characterizations of ideals, prime ideals, and semiprime ideals, and introducing fuzzy ideal extensions.

Contribution

It introduces the concept of Atanassov's intuitionistic fuzzy ideals and their extensions in gamma semigroups, offering new characterization theorems for various types of ideals.

Findings

Characterization of regular gamma semigroups using fuzzy ideals

New criteria for prime ideals in gamma semigroups

Properties of Atanassov's fuzzy ideal extensions

Abstract

The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of gamma semigroups in order to obtain some characterization theorems. We also introduce the notion of Atanassov's intuitionistic fuzzy ideal extension in a gamma semigroup and investigate some of their important properties. A regular gamma semigroup has been characterized in terms of Atanasov's intutionistic fuzzy ideal. Characterization of prime ideal of a gamma semigroup has also been obtained in terms of Atanassov's intutionistic fuzzy ideal extension.